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Questions and Answers
Given the equation $\frac{1}{x + \frac{1}{y + \frac{2}{z + \frac{1}{4}}}}=\frac{29}{79}$, where x, y, and z are natural numbers, what is the value of $2x + 3y - z$?
Given the equation $\frac{1}{x + \frac{1}{y + \frac{2}{z + \frac{1}{4}}}}=\frac{29}{79}$, where x, y, and z are natural numbers, what is the value of $2x + 3y - z$?
- 2
- 1
- 4
- 0 (correct)
If $\frac{1}{x + \frac{1}{y}} = \frac{5}{17}$ and $x$ and $y$ are natural numbers, find the value of $x + y$.
If $\frac{1}{x + \frac{1}{y}} = \frac{5}{17}$ and $x$ and $y$ are natural numbers, find the value of $x + y$.
- 4 (correct)
- 6
- 3
- 5
Given that $x$, $y$, and $z$ are natural numbers and $\frac{1}{x+\frac{1}{y+\frac{1}{z}}} = \frac{41}{130}$, determine the value of $x + y + z$.
Given that $x$, $y$, and $z$ are natural numbers and $\frac{1}{x+\frac{1}{y+\frac{1}{z}}} = \frac{41}{130}$, determine the value of $x + y + z$.
- 6 (correct)
- 8
- 3
- 5
If $\frac{1}{a + \frac{1}{b + \frac{1}{c}}} = \frac{3}{8}$, where $a$, $b$, and $c$ are positive integers, what is the unique ordered triple $(a, b, c)$?
If $\frac{1}{a + \frac{1}{b + \frac{1}{c}}} = \frac{3}{8}$, where $a$, $b$, and $c$ are positive integers, what is the unique ordered triple $(a, b, c)$?
Given that $x$ and $y$ are positive integers, and $\frac{1}{x + \frac{1}{y}} = \frac{7}{30}$, find the values of $x$ and $y$.
Given that $x$ and $y$ are positive integers, and $\frac{1}{x + \frac{1}{y}} = \frac{7}{30}$, find the values of $x$ and $y$.
If $\frac{p}{q} = \frac{1}{3 + \frac{1}{5 + \frac{1}{2}}}$, where $p$ and $q$ are coprime integers, then what is the value of $p + q$?
If $\frac{p}{q} = \frac{1}{3 + \frac{1}{5 + \frac{1}{2}}}$, where $p$ and $q$ are coprime integers, then what is the value of $p + q$?
Given $\frac{1}{5 + \frac{1}{x}} = \frac{a}{b}$, where $x$, $a$, and $b$ are positive integers, find $a+b$ if $x = 3$.
Given $\frac{1}{5 + \frac{1}{x}} = \frac{a}{b}$, where $x$, $a$, and $b$ are positive integers, find $a+b$ if $x = 3$.
If $x$ and $y$ are positive integers such that $\frac{1}{x} + \frac{1}{y} = \frac{1}{4}$, and $x < y$, what is the largest possible value of $y$?
If $x$ and $y$ are positive integers such that $\frac{1}{x} + \frac{1}{y} = \frac{1}{4}$, and $x < y$, what is the largest possible value of $y$?
Suppose $x, y, z$ are positive integers such that $\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 1$. If $x < y < z$, what is the largest possible value of $z$?
Suppose $x, y, z$ are positive integers such that $\frac{1}{x} + \frac{1}{y} + \frac{1}{z} = 1$. If $x < y < z$, what is the largest possible value of $z$?
If $\frac{1}{x + \frac{1}{y + 1}} = \frac{5}{22}$, where $x$ and $y$ are integers, then what is the value of $x + y$?
If $\frac{1}{x + \frac{1}{y + 1}} = \frac{5}{22}$, where $x$ and $y$ are integers, then what is the value of $x + y$?
Flashcards
Continued Fraction
Continued Fraction
A fraction with 1 as the numerator and a sum of an integer and another fraction in the denominator.
Find x, y, and z
Find x, y, and z
Given the equation 1/(x + 1/(y + 1/(z+1/4))) = 29/79, x, y, and z are natural numbers.
Value of x in the Equation
Value of x in the Equation
After inverting and simplifying, x = 2. Then find the reciprocal of the remaining fraction.
Value of y in the Equation
Value of y in the Equation
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Value of z in the Equation
Value of z in the Equation
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Calculating 2x + 3y - z
Calculating 2x + 3y - z
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Study Notes
- The question asks: If 1 / (x + (1 / (y + (2 / (z + (1/4)))))) = 29/79, where x, y, and z are natural numbers, what is the value of 2x + 3y - z?
- Possible answers are 1, 4, 0, or 2
- The question was Answered correctly by the user
- The question has an average time of 01:21
- The question is worth 3 marks
- 20% answered correctly
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